Transport in multilayer graphene: resistance from stacking faults

Abstract

Multilayer graphene exhibits rich possibilities for stacking. While natural bulk graphite predominantly occurs in the Bernal structure, where layers are stacked in an $-ABAB-$ pattern, rhombohedral stacking has sprung to prominence recently. It is well known that Bernal graphite exhibits anisotropic transport, with high resistance to currents along the stacking axis. Careful experiments using pillar geometries have measured out-of-plane resistance, attributing it to stacking faults where planes slip out of the nominal $ABAB$ sequence. The observed resistance shows anomalously large, non-Gaussian, sample-to-sample variations. In this article, we build a theoretical framework to calculate $c$-axis resistance of graphene stacks with an arbitrary stacking arrangement. Our approach builds on the idea that, regardless of stacking sequence, we have in-plane translational symmetry. With in-plane momentum as a good quantum number, $c$-axis transport reduces to an effectively one-dimensional problem that can be addressed using the Landauer paradigm. We calculate the resistances of a variety of simple stacking faults in both Bernal and rhombohedral systems. We also calculate the resistance of a rhombohedral 'slab' embedded between Bernal leads. Remarkably, despite both Bernal and rhombohedral graphite being metallic, the system exhibits insulating behaviour. We attribute this to Fermi surface mismatch. We next calculate the resistance of a multilayer sample with stacking disorder. Resistance is non-self-averaging, akin to a one-dimensional wire where disorder has a strong localizing effect. The median resistance grows exponentially with stack size, indicating insulating character driven by localization. Our results demonstrate that transport measurements on mesoscopic graphitic pillars serve as signatures of stacking faults, and in particular, probe localization-driven physics.